CFA 2018 r17 principles of asset allocation

Level III Principles of Asset Allocation www.ift.world Graphs, charts, tables, examples, and figures are copyright 2017, CFA Institute Reproduced and republished with permission from CFA Institute All rights reserved Contents and Introduction Introduction Developing Asset-Only Asset Allocations Developing Liability-Relative Asset Allocations Developing Goals-Based Asset Allocations Heuristics and Other Approaches to Asset Allocation Portfolio Rebalancing in Practice www.ift.world 2 Developing Asset-Only Asset Allocations Mean–Variance Optimization: Overview Monte Carlo Simulation Criticisms of Mean–Variance Optimization Addressing the Criticisms of Mean–Variance Optimization Allocating to Less Liquid Asset Classes Risk Budgeting Factor-Based Asset Allocation www.ift.world 2.1 Mean–Variance Optimization: Overview When assets are not perfectly correlated they can be combined such that portfolio risk is less than weighted average risk of assets themselves Returns Risks Correlations Focus on asset’s impact on portfolio risk, not the risk of the asset itself Mean-variance optimization (MVO) provides a framework for determining how much to allocate to each asset in order to maximize portfolio’s expected return at a given level of risk “MVO is a risk budgeting tool which helps investors spend their risk budget wisely” www.ift.world Objective Function Expected return and standard deviation are expressed as a percentages The expected return of a given asset mix is 10% and the expected standard deviation is 20% What is the utility of this asset mix for an investor with a risk aversion coefficient of 2? www.ift.world Exhibit 1: Hypothetical UK-Based Investor’s Opportunity Set with Expected Returns, Standard Deviations, and Correlations www.ift.world www.ift.world Exhibit 3: Efficient Frontier Asset Allocation Area Graph—Base Case www.ift.world Example 1: Mean–Variance-Efficient Portfolio Choice An investment adviser is counseling Aimée Goddard, a client who recently inherited €1,200,000 and who has above-average risk tolerance (λ = 2) Because Goddard is young and one of her goals is to fund a comfortable retirement, she wants to earn returns that will outpace inflation in the long term Goddard expects to liquidate €60,000 of the inherited portfolio in 12 months to fund the down payment on a house She states that it is important for her to be able to take out the €60,000 without invading the initial capital of €1,200,000 Exhibit shows three alternative strategic asset allocations Asset Allocation A B C Expected Return 10.00% 7.00 5.25 Standard Deviation of Return 20% 10 Based only on Goddard’s risk-adjusted expected returns for the asset allocations, which asset allocation would she prefer? Recommend and justify a strategic asset allocation for Goddard www.ift.world Determining Allocation to Cash • Include cash among assets for which efficient frontier is constructed • Separate cash from risky assets; define efficient frontier based on ‘risky’ assets ▪ Tangency portfolio ▪ Two fund separation www.ift.world 10 4.3 Constructing Sub-Portfolios Identify pre-optimized sub-portfolio modules best suited to each goal and determine amount to be allocated • Process driven by time horizon and required probability of success • Pick modules that offer highest expected return • Compute dollar amount needed to defease goal A Portfolio Characteristics Expected return Expected volatility 4.3% 2.7% Time Horizon (years) Required Success 99% 90 75 60 2.3% 3.2 3.7 4.1 B C D E 5.5% 6.4% 7.2% 8.0% 4.5% 6.0% 7.5% 10.0% Annualized Minimum Expectation Returns 10 2.2% 3.7 4.6 5.2 2.0% 4.0 5.1 5.9 www.ift.world 1.7% 4.1 5.6 6.6 0.7% 4.0 5.9 7.2 Highest expected return corresponds to lowest “funding cost” F 8.7% 12.5% –0.5% 3.6 6.0% 7.7 46 Example 11: Selecting a Module Address the following module selection problems using Exhibit 36: A client describes a desire to have a reserve of €2 million for business opportunities that may develop when he retires in five years Assume that the word “desire” points to a wish to which the adviser will ascribe a probability of 75% A 70-year-old client with a 20-year life expectancy discusses the need to be able to maintain her lifestyle for the balance of her life and wishes to leave US$3 million to be split among her three grandchildren at her death Expected return Expected volatility Time Horizon (years) 99% 95 90 75 Time Horizon (years) 95% 90 85 75 A 4.3% 2.7% B 5.5% 4.5% C 6.4% 6.0% D 7.2% 7.5% E 8.0% 10.0% F 8.7% 12.5% –0.6% 1.7 2.9 4.9 –2.4% 0.7 2.3 5.0 –4.3% –0.5 1.5 4.9 4.4% 5.0 5.4 6.0 4.4% 5.2 5.7 6.5 4.1% 5.1 5.8 6.8 1.5% 2.3 2.7 3.5 0.9% 2.2 3.0 4.2 0.2% 2.0 3.0 4.6 20 3.3% 3.5 3.7 3.9 3.9% 4.3 4.5 4.9 4.2% 4.7 5.0 5.5 www.ift.world 47 The Smiths have financial assets worth US$25 million The parents are in their mid-fifties, and the household spends about US$500,000 a year They expect that inflation will average about 2% per year for the foreseeable future They express four important goals and are concerned that they may not be able to meet all of them: • They need a 95% chance of being able to maintain their current expenditures over the next five years • They wish to have a 75% chance to be able to create a family foundation, which they wish to fund with US$10 million in 20 years Expected return Expected volatility Time Horizon (years) 99% 95 90 75 Time Horizon (years) 95% 90 85 75 A 4.3% 2.7% B 5.5% 4.5% C 6.4% 6.0% D 7.2% 7.5% E 8.0% 10.0% F 8.7% 12.5% –0.6% 1.7 2.9 4.9 –2.4% 0.7 2.3 5.0 –4.3% –0.5 1.5 4.9 4.4% 5.0 5.4 6.0 4.4% 5.2 5.7 6.5 4.1% 5.1 5.8 6.8 1.5% 2.3 2.7 3.5 0.9% 2.2 3.0 4.2 0.2% 2.0 3.0 4.6 20 3.3% 3.5 3.7 3.9 3.9% 4.3 4.5 4.9 4.2% 4.7 5.0 5.5 www.ift.world 500,000 488,759 510,000 487,325 520,200 485,896 530,604 484,471 541,216 483,050 2,429,502 48 Exhibit 37 Module Selection and Dollar Allocations (US$ thousands) www.ift.world 49 4.4 The Overall Portfolio Overall allocation is the weighted average exposure to each of the asset classes within each module Exhibit 39: Goals-Based Asset Allocation (US$ thousands) Module Required capital in currency As a % of total Cash Global investment-grade bonds Global high-yield bonds Lower-volatility alternatives Global developed equities Global emerging equities Equity-based alternatives Illiquid global equities Trading strategy alternatives Global real estate Total A F D F C 2,430 9.7 80% 20 0 4,978 19.9 1% 6,671 26.7 1% 25 25 2,426 9.7 1% 8,495 34.0 3% 45 11 13 25,000 100.0 9% 24 12 0 0 64 11 20 19 10 64 11 20 13 28 10 100 100 100 100 100 100 www.ift.world 50 4.5 Revisiting the Module Process in Detail Formulate capital market expectations Expected returns Expected variance Correlations Create optimized modules (sub-portfolios) using mean-variance process Mean-variance process is subject to constraints which reflect market portfolio considerations and asset class suitability given goals • Liquidity • Distribution characteristics • Drawdown control Optimal modules not plot on traditional “efficient frontier” because constraints vary from one module to the next www.ift.world 51 Portfolio Characteristics Expected return Expected volatility Expected liquidity Portfolio Allocations Cash Global investment-grade bonds Global high-yield bonds Lower-volatility alternatives Global developed equities Global emerging equities Equity-based alternatives Illiquid global equities Trading strategy alternatives Global real estate Total Constraints Maximum volatility Minimum liquidity Maximum alternatives Minimum cash Maximum HY as a percent of total fixed income Maximum equity spectrum Maximum EM as a percent of public equities Maximum illiquid equities Maximum trading as a percent of equity spectrum Maximum real estate Escrow cash as a percent of illiquid equities Maximum probability of return < drawdown Drawdown horizon Drawdown amount A B C D E F 4.3% 2.7 100.0 5.5% 4.5 96.6 6.4% 6.0 90.0 7.2% 7.5 86.1 8.0% 10.0 83.6 8.7% 12.5 80.0 80% 20 0 0 0 0 100% 26% 44 9 0 100% 3% 45 11 13 13 5 100% 1% 25 25 19 10 100% 1% 34 34 15 100% 1% 64 11 20 0 100% 3.0% 100.0 0.0 80.0 0.0 0.0 15.0 0.0 0.0 0.0 5.0 1.0 0.0 4.5% 95.0 10.0 20.0 10.0 10.0 15.0 0.0 10.0 5.0 5.0 1.5 –5.0 6.0% 90.0 20.0 0.3 20.0 20.0 15.0 5.0 15.0 10.0 5.0 2.0 –7.5 7.5% 85.0 30.0 0.5 50.0 40.0 15.0 10.0 15.0 15.0 5.0 2.0 –10.0 10.0% 80.0 30.0 0.7 100.0 75.0 15.0 15.0 20.0 20.0 5.0 2.5 –15.0 12.5% 70.0 30.0 1.0 100.0 100.0 15.0 20.0 25.0 25.0 5.0 2.5 –20.0 www.ift.world 52 Exhibit 42 Sub-Portfolio Modules Cover a Full Range www.ift.world 53 4.6 Periodically Revisiting the Overall Asset Allocation Goals-based allocation must be regularly reviewed • Time horizon • Rebalancing 4.7 Issues Related to Goals-Based Asset Allocation Hidden goals High level of business management complexity www.ift.world 54 Heuristics and Other Approaches to Asset Allocation Heuristic: rule that provides a reasonable but not necessarily optimal solution Heuristic Comment Critique “120 minus your age” rule 120 – Age = Percentage allocated to stocks Lacks nuances of target date funds’ glide paths 60/40 stock/bond heuristic Provides growth through stocks and risk reduction through bonds Does not consider investor circumstances Endowment model Large allocations to non-traditional investments driven by investment manager skill Complex and high-cost Risk parity Each asset class should contribute equally to total risk Ignores expected returns; contribution to risk is highly dependent on the formation of the investment opportunity set 1/N rule Equal weight to all asset classes Asset classes treated as indistinguishable in terms of returns, volatility and correlations www.ift.world 55 Portfolio Rebalancing in Practice • Rebalancing refers to adjusting portfolio weights to align with strategic asset allocation (SAA) • Since the SAA is the optimal allocation for an investor, a deviation from the SAA represents a cost • Disciplined rebalancing reduces risk and adds to return ▪ Diversification return ▪ Return from being short volatility • Two major strategies: calendar rebalancing and percent-range rebalancing ▪ Calendar rebalancing has a lower cost ▪ Percent-range is a more disciplined risk control policy • Percent-range rebalancing decision: ▪ What is the optimal corridor width? ▪ Rebalance to actual SAA weights or upper/lower edge or somewhere in between? www.ift.world 56 Exhibit 48 Factors Affecting the Optimal Corridor Width of an Asset Effect on Optimal Width of Corridor Factor (All Else Equal) Intuition Factors Positively Related to Optimal Corridor Width The higher the transaction costs, the High transaction costs set a high hurdle Transaction costs wider the optimal corridor for rebalancing benefits to overcome Higher risk tolerance means less sensitivity to divergences from the target allocation Correlation with the rest of the The higher the correlation, the wider When asset classes move in sync, further divergence from target weights portfolio the optimal corridor is less likely Factors Inversely Related to Optimal Corridor Width Volatility of the rest of the The higher the volatility, the Higher volatility makes large divergences from the strategic asset allocation more portfolio narrower the optimal corridor likely Risk tolerance The higher the risk tolerance, the wider the optimal corridor If volatility of an illiquid asset class goes up the rebalancing bands should be widened www.ift.world 57 Example 12: Tolerance Bands for an Asset Allocation An investment committee is reviewing the following strategic asset allocation: • Domestic equities 50% ± 5% (i.e., 45% to 55% of portfolio value) • International equities 15% ± 1.5% • Domestic bonds 35% ± 3.5% The market for the domestic bonds is relatively illiquid The committee views the above corridors as appropriate if each asset class’s risk and transaction cost characteristics remain unchanged The committee now wants to account for differences among the asset classes in setting the corridors Evaluate the implications of the following sets of facts for the stated tolerance bands, given an all-else-equal assumption in each case: Tax rates for international equities increase by 10 percentage points Transaction costs in international equities increase by 20% relative to domestic equities, but the correlation of international equities with domestic equities and bonds declines What is the expected effect on the tolerance band for international equities? The volatility of domestic bonds increases What is the expected effect on their tolerance band? Assume that domestic bonds are relatively illiquid www.ift.world 58 Rebalancing in a Goals-Based Approach “Use of probability- and horizon-adjusted discount rates to size the various goal-defeasing sub-portfolios means that portfolios will usually produce returns that are higher than assumed.” “Sub-portfolios with shorter time horizons for goals with high required probabilities of success will tend to contain relatively low-risk assets, whereas riskier assets may have high allocations in longer-horizon portfolios for goals with lower required probabilities of success.” “Thus, there is a greater chance that the exposure to lower-risk assets will creep up before one experiences the same for riskier assets Thus, failing to rebalance the portfolio will gradually move it down the risk axis—and the defined efficient frontier—and thus lead the client to take less risk than he or she can bear.” www.ift.world 59 Conclusion • Learning objectives • Summary • Examples • Practice problems www.ift.world 60 ... Introduction Developing Asset- Only Asset Allocations Developing Liability-Relative Asset Allocations Developing Goals-Based Asset Allocations Heuristics and Other Approaches to Asset Allocation Portfolio... on asset allocation, the results of two asset allocation exercises are shown, as presented in Exhibit 18 There are a total of asset classes Based on mean–variance analysis, what is the asset allocation. .. the asset allocations, which asset allocation would she prefer? Recommend and justify a strategic asset allocation for Goddard www.ift.world Determining Allocation to Cash • Include cash among assets